Find the sum of [tex]\frac{3b}{b+2}[/tex] and [tex]\frac{12}{b+2}[/tex], and express it in simplest form.
Answer (2)
b + 2 3 b + b + 2 12 = b + 2 3 b + 12 b + 2 3 b + 12 = b + 2 3 b + 6 + 6 = b + 2 3 b + 6 + b + 2 6 = b + 2 3 ( b + 2 ) + b + 2 6 = 3 + b + 2 6
The sum of b + 2 3 b and b + 2 12 simplifies to 3 ⋅ b + 2 b + 4 . No further reduction is possible as the terms in the numerator and denominator do not share common factors. Thus, the final answer is b + 2 3 ( b + 4 ) .
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